1. Field of the Invention
The present invention relates to a method for determining the effects of linear and non-linear loads on electric power systems. More particularly, the present invention relates to a method which determines load current spectra for current flowing in primary conductors which connect power substations to distribution transformers and the load current spectra of current flowing in the secondary windings of the distribution transformers. The method also collects the voltage waveforms at load busses which distribute power to customers and compares the actual substation meter readings with customer metered power and volt-ampere demand, so as to provide electric utilities with information relating to the quality of the supplied power and to facilitate implementation of corrective measures.
2. Description of the Related Art
The quality of electric power supplied by electric utilities is often degraded by harmonics, outages, reduced voltage, flicker, spikes, etc. Most significantly, nonlinear switching-type loads, which introduce harmonics into the system, are a major problem in power quality. Nonlinear devices are not new to electric power systems. Transformers, iron-cored machinery and fluorescent lighting are obvious examples. However, until very recently their nonlinear characteristics were not a problem for electric utilities, since the types of loads which introduce harmonics onto the line were at a minimum and the utilities had developed corrective measures to offset the harmonics generated by those loads. For instance, the ever-present third harmonic was confined to delta-connected windings so that utilities simply had to use delta-wye distribution transformers to reduce the impact of the third harmonic.
Recently new developments in electrical and electronic loads, e.g., in computers, solid-state power conditioners and fluorescent lighting, have brought about a proliferation of power system components and loads having nonlinear characteristics. As a result, the desire to improve the quality of the power supplied to customers has been elevated to a new awareness. One major problem associated with harmonics in the power system is that they reduce the ability of electrical utilities to predict accurately the effects of reducing the voltage during summer peaks in order to reduce the system load.
Practically, the harmonic components of current generated by the non-linear loads create corresponding harmonic components of voltage across the network impedances. As a result, a distortion of the current and voltage waveshapes from sinusoidal occur, thereby rendering the classical power triangle insufficient for power-factor (PF) evaluations.
One way to determine the harmonic content of the power supplied to customers, utilizes a power diagram of the electrical network, shown in FIG. 1, which illustrates the combination of two power-phasor diagrams. The first phasor diagram consists of the two inner gray and pattern filled triangles, which reflects an electrical network that has non-linear loads, and a power supply defined by a sine-wave voltage. In this instance, the fundamental rms value of the phase voltage V.sub.1 is the same as the total rms value of the voltage (V.sub.rms) and is represented below in equation one (1): EQU V.sub.1 =V.sub.rms ( 1)
The rms value of the phase current, which in this instance has a high harmonic content, is represented by: ##EQU1## where n denotes the current harmonic number. In the gray-filled triangle of FIG. 1, the active power (P.sub.1) per phase is represented in equation three (3) below. The active power (P.sub.1) relates to the fundamental components of the voltage (V.sub.1), the current (I.sub.1), and the phase angle .phi. between V.sub.1 and I.sub.1 : EQU P.sub.1 =V.sub.1 I.sub.1 cos .phi..sub.1 [W] (3)
A wattmeter is utilized to measure the active (or real) power (P.sub.1). The reactive power Q.sub.1 per phase, represented in equation four below, also relates to the fundamental values of voltage (V.sub.1), the current (I.sub.1), and the phase angle .phi..sub.1 between V.sub.1 and I.sub.1 : EQU Q.sub.1 =V.sub.1 I.sub.1 sin .phi..sub.1 [var] (4)
A varmeter is utilized to measure the reactive power Q.sub.1. The apparent power S.sub.1 is defined by: ##EQU2## and is also a function of the fundamental components of the voltage V.sub.1 and current I.sub.1. The apparent power is a calculated quantity often used as a rating unit and it cannot be measured by standard meters. One of the reasons is that the current harmonics generated by non-linear loads introduce an additional distortion power D.sub.s represented in equation six (6) below which prevents accurate readings: EQU D.sub.s =V.sub.rms I.sub.ac [VA] (6)
Multiplying both sides of equation two (2) above by V.sub.rms, the total power in volt-amperes [VA].sub.s can be obtained, and is represented by equation seven (7) below: EQU [VA].sub.s.sup.2 =(V.sub.rms I.sub.rms).sup.2 =S.sub.1.sup.2 +D.sub.s.sup.2 [VA] (7)
Equation seven (7) can be illustrated such that the three phasors [VA].sub.s, S.sub.1 and D.sub.s constitute a right-angle triangle, and is shown in FIG. 1 by the pattern-filled triangle. The product of the readings of input ac voltmeter and ac ammeter provides the total [VA].sub.s.
The power factor PF is defined as the ratio of active power (P.sub.1) per total voltamperes ([VA].sub.s) and is represented in equation eight (8) below. As can be seen from equation eight (8), the actual power factor PF does not agree with the classical representation of the power factor, i.e. PF.noteq.cos .phi..sub.1. This is due to the harmonic components caused by the load. ##EQU3##
The second phasor diagram shown in FIG. 1 is the outer diagram. The second phasor diagram relates to an electrical network having nonlinear loads which are supplied by a distorted voltage wave. The two phasor diagrams of FIG. 1, i.e., the inside and the outside diagrams, correspond to loads that have the same fundamental voltage (V.sub.1), current, (I.sub.1), and phase angle (.phi..sub.1). The total rms value of the voltage in this case is represented below in equation nine (9): ##EQU4## where m denotes the voltage harmonic number. The rms value of the current is represented by equation two (2). In instances where n=m, i.e. when the same harmonic component is present in both the current and the voltage, the product power which is represented as the voltage times the current will introduce average values per cycle for the total active and reactive power for the harmonic components, as represented by equation ten (10) below: ##EQU5## Generally, a standard wattmeter is utilized to measure P.sub.1 +P.sub.H. A digital varmeter is needed to measure Q.sub.1 +Q.sub.H. With these known values, it is possible to calculate a value for the apparent harmonic power S.sub.1H as shown in equation eleven (11) below: ##EQU6## However, as noted above, the apparent power is a calculated quantity often used as a rating unit, and does not provide suitable information in analyzing the system behavior. Furthermore, a supplemental harmonic distortion power D.sub.H prevails due to the product of other harmonics where m.noteq.n, and this value also cannot be measured.
The total power of the network in volt-amperes is represented below in equation twelve (12): EQU [VA].sub.T =V.sub.rms I.sub.rms [VA] (12)
Currently, the total volt-ampere power can be obtained by multiplying the measured value of an ac voltmeter by the measured value of an ac ammeter. The power factor PF is represented below in equation thirteen (13): ##EQU7##
Generally, the parameters of interest to electric utilities in determining the quality of the power supplied to customers include:
(1) the effective (active) power P=P.sub.1 +P.sub.H ; PA1 (2) the effective harmonic power P.sub.H ; PA1 (3) the fundamental reactive power Q.sub.1 ; and PA1 (4) the total power [VA].sub.T.
The effective power (P) and the total power ([VA].sub.T) define the power factor (PF) for the system, i.e., PF=P/[VA].sub.T. The fundamental reactive power Q.sub.1, is the dominant component of the reactive power, which when Q.sub.1 exceeds a predefined value alerts an electric utility to an extreme demand in reactive power. The harmonic power (P.sub.H) indicates the amount of harmonics polluting the network which permits an electric utility to assess the need for special filters or other measures to decrease the effects of the harmonic power.
For linear loads, the values of P.sub.1, Q.sub.1 and S.sub.1 for an individual load are easily ascertained from measurements obtained from standard meters, e.g, a wattmeter, a voltmeter and an ammeter. For a linear composite load, the active power in watts and the reactive power VARs for individual loads may be added to find the total P.sub.1 and Q.sub.1, and hence the total apparent power S.sub.1. However, for nonlinear loads, the harmonic components of current in the individual loads must be summed taking their phases into account. This phase information is essential and cannot be retrieved by standard meters, e.g., wattmeter, varmeter, voltmeter or ammeter. Furthermore, this phase information cannot be retrieved even if the harmonic content of an individual load is measured by a spectrum analyzer.
Therefore, a need exists for a system which determines the current harmonic components for a plurality of loads which may be connected to power conductors, which collects substation voltage, current and power quantities, which calculates the actual load voltage taking into account the harmonic load characteristics and which compares the collected values to the actual values derived from the actual load voltage, to determine the effects of the harmonics on the power supplied to customers.